I think part of my problem is that the camera that I use has too wide of an in-focus 'box'. So even if I've zoomed into a tree, for example, the in-focus box ALSO includes the houses that are 200'+ behind the tree.

I really doubt that is part of problem. This is one place that pixel peeping is a useful diagnostic tool. Presuming you wanted the tree in focus blow the photo up to 100% and visually scan for the plane of focus. I suspect that the tree will be in better focus than the houses. The system is looking for best contrast and I suspect it will find it on the edge of the trunks. Look for a test photo that was near wide open for the focal length in use.

If you can't find a plane of focus I'd suspect the lens was stopped down quite a ways.

For most photographic purposes in the range where both camera have the same focal length they will have the essentially the same DoF. The SX30IS has much longer focal lengths available and those longer focal lengths can, under some realist scenarios provide a very shallow DoF but whether or not you'd be able bring that to bear in the your photographic circumstances I can't predict.

To significantly change the DoF characteristic you'll need cameras with much larger sensors than 1/2.3 use in both the 30 or the 130. At least a 4:3 or m4:3 system.